A unified study on mechanical characterization and correlation with microstructures of three major varieties of polyurethane foam namely, viscoelastic (VE), high resilience (HR), and semi-rigid (SR), with engineering design applications in mind has been reported here. Cubical foam samples of VE, HR and SR varieties and different densities are tested under compressive loading. The recorded force-displacement data is used to clarify the distinct behaviors of short-term and long-term recovery of VE and HR foams, and crushability of SR foam. It is pointed out that foam of a given type can be suitable for a particular engineering design application based on its recoverability, strength and energy-absorption attributes. A possible relation between foam cellular structure and its mechanical behavior has been discussed.